Stability of cosmological solutions in f ( R ) models of gravity

By I. Sawicki, Wayne Hu. 2007

187 citations recorded by the source corpus.

We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the Ricci scalar, $f(R)$. Using the example of $f(R)=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}^{4}/R$ we show that only such choices of $f(R)$ where ${\mathrm{d}}^{2}f/\mathrm{d}{R}^{2}g0$ have stable high-curvature limits and well-behaved cosmological solutions with a proper era of matter domination. The remaining models enter a phase dominated by both matter and scalar kinetic energy where the scalar curvature remains low.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/890334344ac08c65368a356ce93efe0e5ef47e18

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Citations in the corpus

Dynamical systems applied to cosmology: Dark energy and modified gravity (2017, methodology): “Sawicki & Hu (2007) showed that viable f(R) cosmological models should satisfy f,RR > 0 and then made an example with the theory f(R) = R + α/R. Models with (inverse) power-law corrections to the Einstein-Hilbert Lagrangian were also considered by Clifton (2008) who delivered an asymptotic analysis…”
f(R) Theories (2010, background): “The existence of the latter phase gives rise to the modification to the matter power spectrum [146, 74, 544, 526, 251] (see also [597, 493, 494, 94, 446, 278, 435] for related works).”
Approaches to understanding cosmic acceleration (2009, background): “Classically, fRR > 0 is required to keep the evolution in the high-curvature regime stable against small perturbations [162, 163].”
f(R) Theories Of Gravity (2008, background): “The stability condition f ′′ ≥ 0 is recovered in studies of cosmological perturbations (Sawicki and Hu, 2007).”